JETP Letters

, Volume 106, Issue 10, pp 637–642 | Cite as

Gravitational lensing of a star by a rotating black hole

  • V. I. DokuchaevEmail author
  • N. O. Nazarova
Astrophysics and Cosmology


The gravitational lensing of a finite star moving around a rotating Kerr black hole has been numerically simulated. Calculations for the direct image of the star and for the first and second light echoes have been performed for the star moving with an orbital period of 3.22 h around the supermassive black hole SgrA* at the center of the Galaxy. The time dependences for the observed position of the star on the celestial sphere, radiation flux from the star, frequency of detected radiation, and major and minor semiaxes of the lensed image of the star have been calculated and plotted. The detailed observation of such lensing requires a space interferometer such as the Russian Millimetron project.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. L. Fish, K. Akiyama, K. L. Bouman, et al. (Event Horizon Telescope Collab.), Galaxies 4, 54 (2016).ADSGoogle Scholar
  2. 2.
    T. Lacroix and J. Silk, Astron. Astrophys. 554, A36 (2013).ADSGoogle Scholar
  3. 3.
    T. Johannsen, A. E. Broderick, P. M. Plewa, S. Chatzopoulos, S. S. Doeleman, F. Eisenhauer, V. L. Fish, R. Genzel, O. Gerhard, and M. D. Johnson, Phys. Rev. Lett. 116, 031101 (2016).ADSGoogle Scholar
  4. 4.
    A. E. Broderick P. M. Plewa, S. Chatzopoulos, S. S. Doeleman, F. Eisenhauer, V. L. Fish, R. Genzel, O. Gerhard, and M. D. Johnson, Astrophys. J. 820, 137 (2016).ADSGoogle Scholar
  5. 5.
    A. A. Chael, M. D. Johnson, R. Narayan, S. S. Doeleman, J. F. C. Wardle, and K. L. Bouman, Astrophys. J. 829, 11 (2016).ADSGoogle Scholar
  6. 6.
    J. Kim, D. P. Marrone, C. Chan, L. Medeiros, F. Özel, and D. Psaltis, Astrophys. J. 832, 156 (2016).ADSGoogle Scholar
  7. 7.
    F. Roelofs, M. D. Johnson, H. Shiokawa, S. S. Doeleman, and H. Falcke, arXiv:1708.01056 [astro-ph.HE].Google Scholar
  8. 8.
    S. Doeleman, Nat. Astron. 1, 646 (2017).ADSGoogle Scholar
  9. 9.
    J. M. Bardeen, in Black Holes, Ed. by C. de Witt and B. S. de Witt (Gordon and Breach, New York, 1973), p. 215.Google Scholar
  10. 10.
    S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon, Oxford, 1983).zbMATHGoogle Scholar
  11. 11.
    H. Falcke, F. Melia, and E. Agol, Astrophys. J. 528, L13 (2000).ADSGoogle Scholar
  12. 12.
    R. Takahashi, Astrophys. J. 611, 996 (2004).ADSGoogle Scholar
  13. 13.
    H. Falcke and S. Markoff, Class. Quantum Grav. 30, 244003 (2013).ADSGoogle Scholar
  14. 14.
    Z. Li and C. Bambi, J. Cosmol. Astropart. Phys. 01, 041 (2014).ADSGoogle Scholar
  15. 15.
    P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, Phys. Rev. Lett. 115, 211102 (2015).ADSGoogle Scholar
  16. 16.
    A. A. Abdujabbarov, L. Rezzolla, and B. J. Ahmedov, Mon. Not. R. Astron. Soc. 454, 2423 (2015).ADSGoogle Scholar
  17. 17.
    Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya, and Y. Mizuno, Phys. Rev. D 94, 084025 (2016).ADSMathSciNetGoogle Scholar
  18. 18.
    R. Takahashi, Publ. Astron. Soc. Jpn. 57, 273 (2005).ADSGoogle Scholar
  19. 19.
    R. Takahashi and K. Watarai, Mon. Not. R. Astron. Soc. 374, 1515 (2007).ADSGoogle Scholar
  20. 20.
    S. Doeleman, J. Weintroub, A. E. E. Rogers, et al., Nature 455, 78 (2008).ADSGoogle Scholar
  21. 21.
    F. de Paolis, G. Ingrosso, A. A. Nucita, A. Qadir, and A. F. Zakharov, Gen. Rel. Grav. 43, 977 (2011).ADSGoogle Scholar
  22. 22.
    L. Yang and Z. Li, Intern. J. Mod. Phys. D 25, 1650026 (2016).ADSGoogle Scholar
  23. 23.
    P. J. Armitage and C. S. Reynolds, Mon. Not. R. Astron. Soc. 341, 1041 (2003).ADSGoogle Scholar
  24. 24.
    J. Dexter, E. Agol, P. C. Fragile, and J. C. McKinney, Astrophys. J. 717, 1092 (2010).ADSGoogle Scholar
  25. 25.
    M. D. Johnson, V. L. Fish, S. S. Doeleman, A. E. Broderick, J. F. C. Wardle, and D. P. Marrone, Astrophys. J. 794, 150 (2014).ADSGoogle Scholar
  26. 26.
    O. J. E. von Tunzelmann, P. Franklin, and K. S. Thorne, Class. Quantum Grav. 32, 065001 (2015).ADSGoogle Scholar
  27. 27.
    D. Psaltis, R. Narayan, V. L. Fish, A. E. Broderick, A. Loeb, and S. S. Doeleman, Astrophys. J. 798, 15 (2015).ADSGoogle Scholar
  28. 28.
    V. L. Fish, M. D. Johnson, and R. Lu, Astrophys. J. 795, 134 (2014).ADSGoogle Scholar
  29. 29.
    T. Johannsen, C. Wang, A. E. Broderick, S. S. Doeleman, V. L. Fish, A. Loeb, and D. Psaltis, Phys. Rev. Lett. 117, 091101 (2016).ADSGoogle Scholar
  30. 30.
    A. E. Broderick and A. Loeb, Astrophys. J. 697, 1164 (2009).ADSGoogle Scholar
  31. 31.
    A. E. Broderick, A. Loeb, and M. J. Reid, Astrophys. J. 735, 57 (2011).ADSGoogle Scholar
  32. 32.
    S. S. Doeleman, F. V. Fish, D. E. Schenck, et al., Science 338, 355 (2012).ADSGoogle Scholar
  33. 33.
    T. Johannsen, D. Psaltis, S. Gillessen, D. P. Marrone, F. Ozel, S. S. Doeleman, and V. L. Fish, Astrophys. J. 758, 30 (2012).ADSGoogle Scholar
  34. 34.
    M. Inoue, J. C. Algaba-Marcos, K. Asada, et al., Radio Sci. 49, 564 (2014).ADSGoogle Scholar
  35. 35.
    A. E. Broderick, R. Narayan, J. Kormendy, E. S. Perlman, M. J. Rieke, and S. S. Doeleman, Astrophys. J. 805, 179 (2015).ADSGoogle Scholar
  36. 36.
    T. Lacroix, M. Karami, A. E. Broderick, J. Silk, and C. Boehm, Phys. Rev. D 96, 063008 (2017).ADSGoogle Scholar
  37. 37.
    K. Akiyama, K. Kuramochi, S. Ikeda, et al., Astrophys. J. 838, 1 (2017).ADSGoogle Scholar
  38. 38.
    V. P. Frolov and I. L. Shapiro, Phys. Rev. D 80, 044034 (2009).ADSMathSciNetGoogle Scholar
  39. 39.
    A. E. Broderick, A. Loeb, and R. Narayan, Astrophys. J. 701, 1357 (2009).ADSGoogle Scholar
  40. 40.
    D. Borka, P. Jovanovic, V. B. Jovanovic, and A. F. Zakharov, J. Cosmol. Astropart. Phys. 11, 050 (2013).ADSGoogle Scholar
  41. 41.
    L. Amarilla and E. F. Eiroa, Phys. Rev. D 87, 044057 (2013).ADSGoogle Scholar
  42. 42.
    A. F. Zakharov, arXiv:1407.2591.Google Scholar
  43. 43.
    A. F. Zakharov, D. Borka, V. B. Jovanovic, and P. Jovanovic, Adv. Space Res. 54, 1108 (2014).ADSGoogle Scholar
  44. 44.
    S. Wei, P. Cheng, Y. Zhong, and X. Zhou, J. Cosmol. Astropart. Phys. 08, 004 (2015).ADSGoogle Scholar
  45. 45.
    B. P. Singh and S. G. Ghosh, arXiv:1707.07125 [gr-qc].Google Scholar
  46. 46.
    S. B. Giddings and D. Psaltis, arXiv:1606.07814 [astroph.HE].Google Scholar
  47. 47.
    J. R. Mureika and G. U. Varieschi, arXiv:1611.00399[grqc].Google Scholar
  48. 48.
    A. F. Zakharov, P. Jovanovic, D. Borka, and V. B. Jovanovic, J. Cosmol. Astropart. Phys. 05, 045 (2016).ADSGoogle Scholar
  49. 49.
    M. Amir, B. P. Singh, and S. G. Ghosh, arXiv:1707.09521[gr-qc].Google Scholar
  50. 50.
    O. Y. Tsupko, Phys. Rev. D 95, 104058 (2017).ADSMathSciNetGoogle Scholar
  51. 51.
    N. S. Kardashev, I. D. Novikov, and A. A. Shatskiy, Int. J. Mod. Phys. D 16, 909 (2007).ADSGoogle Scholar
  52. 52.
    A. A. Shatskiy, I. D. Novikov, and N. S. Kardashev, Phys. Usp. 51, 457 (2008).ADSGoogle Scholar
  53. 53.
    E. O. Babichev, V. I. Dokuchaev, and Yu. N. Eroshenko, Phys. Usp. 56, 1155 (2013).ADSGoogle Scholar
  54. 54.
    V. I. Dokuchaev, Gen. Relativ. Grav. 46, 1832 (2014).ADSGoogle Scholar
  55. 55.
    V. I. Dokuchaev and Yu. N. Eroshenko, JETP Lett. 101, 777 (2015).ADSGoogle Scholar
  56. 56.
    V. I. Dokuchaev and Yu. N. Eroshenko, Phys. Usp. 58, 772 (2015).ADSGoogle Scholar
  57. 57.
    A. Herrera-Aguilar and U. Nucamendi, Phys. Rev. D 92, 045024 (2015).ADSGoogle Scholar
  58. 58.
    R. Becerril, S. Valdez-Alvarado, and U. Nucamendi, Phys. Rev. D 94, 124024 (2016).ADSGoogle Scholar
  59. 59.
    C. M. Will and M. Maitra, Phys. Rev. D 95, 064003 (2017).ADSGoogle Scholar
  60. 60.
    F. Ferrer, A. M. da Rosa, and C. M. Will, arXiv:1707.06302 [astro-ph.CO].Google Scholar
  61. 61.
    C. Goddi, H. Falcke, M. Kramer, et al., Int. J. Mod. Phys. D 26, 1730001 (2017).ADSGoogle Scholar
  62. 62.
    N. S. Kardashev, I. D. Novikov, V. N. Lukash, S. V. Pilipenko, E. V. Mikheeva, D. V. Bisikalo, D. S. Wiebe, A. G. Doroshkevich, A. V. Zasov, I. I. Zinchenko, P. B. Ivanov, V. I. Kostenko, T. I. Larchenkova, S. F. Likhachev, I. F. Malov, et al., Phys. Usp. 57, 1199 (2014).ADSGoogle Scholar
  63. 63.
    A. C. Fabian, M. J. Rees, L. Stella, and N. E. White, Mon. Not. R. Astron. Soc. 238, 729 (1989).ADSGoogle Scholar
  64. 64.
    A. F. Zakharov, F. de Paolis, G. Ingrosso, and A. A. Nucita, New Astron. 10, 479 (2005).ADSGoogle Scholar
  65. 65.
    L. W. Brenneman and C. S. Reynolds, Astrophys J. 652, 1028 (2006).ADSGoogle Scholar
  66. 66.
    A. F. Zakharov and S. V. Repin, New Astron. 11, 405 (2006).ADSGoogle Scholar
  67. 67.
    J. M. Miller, Ann. Rev. Astron. Astrophys. 45, 441 (2007).ADSGoogle Scholar
  68. 68.
    K. S. Virbhadra, Phys. Rev. D 79, 083004 (2009).ADSGoogle Scholar
  69. 69.
    S. S. Doeleman, V. L. Fish, A. E. Broderick, A. Loeb, and A. E. E. Rogers, Astrophys. J. 695, 59 (2009).ADSGoogle Scholar
  70. 70.
    V. Perlick and O. Yu. Tsupko, Phys. Rev. D 95, 104003 (2017).ADSMathSciNetGoogle Scholar
  71. 71.
    A. G. Polnarev, Sov. Astrophys. 8, 273 (1972).ADSGoogle Scholar
  72. 72.
    C. T. Cunnungham and J. M. Bardeen, Astrophys. J. 173, L137 (1972).ADSGoogle Scholar
  73. 73.
    C. T. Cunnungham and J. M. Bardeen, Astrophys. J. 183, 237 (1973).ADSGoogle Scholar
  74. 74.
    J.-P. Luminet, Astron. Astrophys. 75, 228 (1979).ADSGoogle Scholar
  75. 75.
    B. Carter, Phys. Rev. 174, 1559 (1968).ADSGoogle Scholar
  76. 76.
    J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Astrophys. J. 178, 347 (1972).ADSGoogle Scholar
  77. 77. Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  1. 1.Institute for Nuclear ResearchRussian Academy of SciencesMoscowRussia
  2. 2.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

Personalised recommendations